curve #6223

y² + xy = x³ − 342240928070465111564621569807549895x + 57710313047687708457420640902405280725758605424905737

a-invariants: [1, 0, 0, -342240928070465111564621569807549895, 57710313047687708457420640902405280725758605424905737]
c-invariants: [16427564547382325355101835350762394961, -49861710473202180131852780560751650579708188113262149209]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 1625092983846624019990514181306541421750465189661625565780175348476375084610801332910
discriminant (Δ): 1126754927078861852469147972120357250933385171741087250739032798466885949279507770250842451060898240768000000
Faltings height: 19.4429
naive height: 257.0761
primes of bad reduction: 2, 3, 5, 7, 11, 19, 107, 389, 523, 16987, 460767635513915583751, 217309600450855630187436721628202412252112050903
regulator: 1220007208122044087214584.7221964095216837605335056163648018538683558732657840585856778
submitted by: apkorte
submitted at: 2026-10-31 02:22:21 UTC
last updated: 2026-10-31 02:22:21 UTC

(471664596437173414, 34891595299384249381340293)
(824046684940135414, 579015659194788192478304293)
(4731762189656081974, 10216674827468706608832659173)
(2167471123571448031/4, -1416803697370077393743539531/8)
(-509577713934145526, 315890645641730505340101673)
(28626990110454514, 218943931925888996331172093)
(567585021248898214, -215194255952175457379371307)
(3241340412781308969574/5041, 115141186383436418482615590601523/357911)
(855247528554519844, 624963187291161240555128983)
(688349826143792374, -385079886421597486392662747)
(5816107619105861376966/169, 443492420666070964830266857763721/2197)
(-2030367508671962186/25, -36436938092898053251825796623/125)
(1545037727922793974, -1793644048855004120882589147)
(636092093240022931/4, -683873737532386053882807481/8)
(168685929916649014, 69130545647203392171377893)
(71416191516594934, -183393051744495674434373147)
(162674717511789814, -79631891730345882694177307)
(470156509869837814, -27023441993436857968148507)
(983679060846750214, 820296916841375313169264693)
(211324500824586319426/289, 2188552434231267023242903619789/4913)
(-779938622029490176244/1849, -28336158373978396632105319311569/79507)
(733549330526471734, -448752335040831071652296987)
(1662092674824067050416566/10975969, -3517520945541836412010903154835144779/36363385297)
(-325429195643419340954/6889, -155303079494033997631460478666409/571787)

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